1. Introduction

Amonst the major challenges in micro-engineering technologies today are the identification of appropriate materials for efficient micron-sized motors and the development of methods for their fine control and regulation. To this end, the use of optical forces to generate rotary motion affords the obvious important advantage of the possibility of contact-less motion. The broad approaches that are presently in vogue involve (i) exploiting the optical-field-induced motion of specially shaped dielectrics [1] and birefringent particles [2], (ii) using specially shaped laser beams [3] or circularly polarized laser light to generate optical forces that induce rotational motion in materials like quartz [4], and (iii) adopting a biological approach by utilizing protein motors which normally utilize chemical energy within the cell to function as a motor [5]. A continuing problem with proteins as rotary machines is that they require extremely well-controlled environments, and their dependence on chemical sources of energy does not readily allow for external fine control. While optically-generated forces that form the backbone of the other two approaches do not suffer from these disadvantages, there are very stringent constraints on the possible shapes that such motors can assume, and the micro-fabrication of such shapes and materials continues to be a key challenge [1–3, 6]. An ideal system would require that we identify material which is not difficult to fabricate and which can be controlled with precision. The results of experiments we report here lead us to believe that generating such a system might, indeed, be possible. We use an optical trap of the type pioneered by Ashkin and coworkers [7] in conjunction with naturally occurring, cellular material that possesses an internal chemical motor. The interplay between optically induced forces and ones that are generated internally within the trapped cell is utilized to obtain rotary motion over which control is exercised in relation to both speed as well as direction of rotation.

We have used an optical trap to conduct experiments on live cells of Chlamydomonas reinhardtii, which is an autotrophic, biflagellated, unicellular, eukaryotic organism, 7–10 µm in diameter, and capable of autonomous motion using it’s flagella [8] that are powered by dynein motors. Fig. 1(a) is a picture of a Chlamydomonas cell that has been stained with a synthetic dye; the two flagella protruding from the cell body are clearly visible. Each flagellum comprises a microtubular axoneme enclosed in a lipid bilayer (plasma membrane) and a basal body complex. The axonemes are cylindrical structures ranging from 10–12 µm in length and ~0.5 µm in diameter. As depicted in Fig. 1(b), axonemes have a 9+2 arrangement: they are composed of 9 outer doublet microtubules forming an outer ring that surrounds two central microtubules. Force generation is due to the dynein motor complexes that are situated at the junction between two adjacent microtubule doublets [9].

 

Fig. 1. (a) Image of a wild-type Chlamydomonas cell stained with a synthetic dye, depicting the cell body (long diameter ~10 µm) and two flagella; (b) cartoon representation of the cross section (proximal to the cell body) of a single axoneme of the flagella (see text).

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2. Experimental details

The single beam optical trap used by us [10,11] consisted of a 1064 nm, 1 W diode pumped Nd:YVO₄ laser used in conjunction with a 100X oil-immersed objective of large numerical aperture (NA=1.3). Very tight focusing of the linearly-polarized laser light produced a spatially-sharp intensity gradient; any dielectric material placed in the vicinity of the laser focal volume experiences a force directed towards the region of maximum light intensity. The diameter of the trapping volume was measured to be ~1 µm; its depth was dependent on the incident laser power. Real-time images of the dynamics of trapped cells were recorded using a CCD camera. The cells used in our experiments were cultured in Tris-Acetate Phosphate (TAP) medium [8] and harvested in mid-log phase with cell densities of ~10⁵ ml^-1. The cells were resuspended and diluted using fresh TAP medium to a final concentration of ~10³ cells ml^-1. About 10 µl of this solution was added to a microscope coverslip containing 190 µl of TAP medium.

3. Results and discussion

The strong focussing of the laser light generates a gradient force, F_g, which exerts a pull on Chlamydomonas cells towards the focal zone. On the other hand, there are scattering forces, F_s, which push the cells away from the focus, towards the incident light direction. The magnitude of the total force that is generated in optical traps is F_trap=(${\mathrm{F}}_{\mathrm{s}}^2$+${\mathrm{F}}_{\mathrm{g}}^2$)^1/2. When F_g>F_s, a cell is trapped. For laser power P (typically 10–30 mW in our experiments), the momentum of the light beam that is experienced per second, F_trap~P n/c (where n is the refractive index of the solvent in which the cells float, and c is the speed of light in vacuum), is in the range of ~10 pN.

For a given value of incident laser power, the trapping force was measured using a flow technique that has been recently described [10]. For any cell undergoing normal, flagellar-based translational motion in the vicinity of the laser focal volume, the optical trap acted as a “pivot”, converting the translational motion of the cell into rotary motion about the focal spot. On removal of the trap, rotary motion stopped and the cell restarted its translational motion, indicating that the optical radiation used in the experiments causes no discernable damage to the cellular motor system.

Typical rotation of a trapped cell is depicted in Fig. 2a. A large number of cells were analyzed at different times of the day to account for possible temperature- and time-dependent variations. No such variations were found. The cells were trapped one at a time, and their rotational speed was determined by the number of frames of a real-time movie that brought a rotating cell back to a given starting position. Rotational speeds were measured to be in the range of 60–100 rpm. Using a classical fluid dynamics approach [12] that is appropriate to the low-turbulence conditions in our experiment, these rotation speeds were used to deduce values of torque, τ, that acts on a spherical particle of radius r rotating with angular velocity ω:

τ=-8πηr ³ ω,

where η is the viscosity of the medium. We obtain torque values in the range 7500 to 12000 pN nm for our rotating Chlamydomonas cells.

As discussed in the following, we could change the rotation speed by varying the optical force. The direction of cell rotation could also be changed from clockwise (CW) to counterclockwise (CCW), or vice versa, by varying the trapping force. For certain values of trapping force, we could stop cell rotation altogether.

Analysis of our data indicates that for the same trapping force, the rotational speeds in the CW and CCW direction were similar. Based on our monitoring of a large number of trapped cells, we believe that a cell that is capable of translational motion by virtue of flagellar action powered by the cell’s in-built motor gets “tipped” into either CW or CCW rotation in stochastic fashion. However, following such an initial stochastic event, subsequent cellular rotation appears to be strictly under the control of the optical-field in the following manner: a trapped cell that was initially rotating CW (or CCW) changes its rotational speed as the trapping force is changed (by altering the focus position); for a specific value of the optical force the flagellar motor force is annulled and the cell stops rotating. Beyond this value of optical force, the trapped cell reverses the direction of its rotation. In terms of optical parameters we note that within the trap the cell experiences two types of forces. One is F_trap and the other is generated by the internal dynein motors in the flagella, F_flagella. When F_trap acts in the same direction as F_flagella the rotational speed of the cell increases (Fig. 2(b)). When F_trap acts in the opposite direction to F_flagella the rotational speed decreases; it may even result in the complete stopping of the rotation and reversal of direction of rotation (Fig. 2(c)).

 

Fig. 2. (a) Real time movie showing rotation of trapped Chlamydomonas cells (1.57 MB). (b) Movie showing changes in the rotational speed of the trapped cell (1.17 MB). (c) Movie showing that cell rotation can be made to change from clockwise to counterclockwise by varying the trapping force (1.87 MB).

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In our experiments we established the specific value of trapping force, F_trap, at which cellular rotation ceased just before the reversal in rotational direction. We took this value of force to represent a situation where cellular motion driven by the flagellar motor system was countered by an equal and opposite force generated by the optical field. This indicates that it is readily possible to control both the speed and sense of rotation externally, in effect, “engineering” the motion of a cell in the trap by controlling the optically induced force that is responsible for the pivot-like action on a moving cell that we alluded to above.

Very recent work on red blood corpuscles (RBC’s) [11] has indicated that rotation in an optical trap can be induced by changes in cell shape and ion gradients. The present work is a qualitative extension in that, unlike RBCs which do not possess any internal means of motion, the trapped cells in these experiments do, indeed, have intrinsic capability for linear motion. Unlike RBCs, the cells used in the present study do not undergo any changes in shape and hence, the induced rotary action that is observed depends on the intrinsic motoring action of the cell. To explore the interplay of forces that are internally generated by chemical means with those that are externally generated by means of an optical field, we studied rotation in trapped Chlamydomonas cells under conditions in which the cell’s flagellar system was altered, either reversibly or permanently. Three different types of experiments were conducted:

(1) Treatment with 0.01% glacial acetic acid is known to induce reversible deflagellation without affecting the viability of the cells [8]. Glacial acetic acid was diluted using TAP medium to 0.01%, and this solution was added, in 1:1 ratio, to a suspension of Chlamydomonas cells in TAP medium. As expected there is no translational motion, reflecting the consequences of deflagellation; this was confirmed by staining the cells for flagella. Such cells were then immediately trapped and their motion (or lack thereof) was observed. We found that wild type cells, when subject to such acid treatment, did not rotate in the trap. It is pertinent to note that, as is well known in biology [8], acid-induced deflagellation is temporary; flagella re-growth was observed on timescales of 15–20 minutes, following which these cells exhibited rotary action upon trapping.

(2) A method that is known to inhibit flagellar function without recourse to deflagellation involves administration of Ni²⁺ ions [13]. Chlamydomonas cells were treated with NiCl at a final concentration of 1 mM. The cells were then trapped and their motion was studied. Ni-administered trapped cells ceased to move translationally and, consequently, also ceased to rotate. It is possible to reverse this inhibition by administration of excess Ca²⁺ ions. Post Ni²⁺ treatment, the cells were pelleted and re-suspended in TAP medium supplemented with 10 mM Ca²⁺ and incubated on a shaker under continuous light for 12 hours. These cells were then trapped and their motion under the trap was studied to score for recovery of rotation. Restoration of cellular rotation was, indeed, observed (Fig. 3). Untrapped cells demonstrated normal translational motion.

 

Fig. 3. Addition of Ni²⁺ ions to wild type Chlamydomonas cells renders the flagella immotile; cell rotation ceases. Subsequent addition of excess Ca²⁺ ions restores cell rotation. Acid-shocked cells behaved identically to nickel treated ones.

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(3) In order to unravel the biological basis of the role of flagella vis-à-vis rotary action, we also used a mutant strain in which the flagella are absent and discovered that these also did not rotate in the trap. Typical rotational frequencies measured with wild type cells (denoted cc-125 in Fig. 4) and those with no flagellar action (cc-407) are depicted in Fig. 4.

Taken together, these results indicate that a functional flagellar motor system is necessary, perhaps even sufficient for rotation in the trap. Taking cognizance of these premises, we have experimentally determined that the flagellar motor force associated with a trapped rotating live cell is ~10 pN, and the resultant torque that arises from this is ~12000 pN nm. This value of 10 pN is a net force that is generated, per beat cycle of flagella, as the cell moves in unconstrained fashion.

To put such force value in perspective, it is of interest to consider that a stalled axoneme of a bull sperm, with a lever arm that is 12 µm long, has been shown to generate a torque of ~3000 nN nm [14]. Were a similar value of torque to be generated in Chlamydomonas a rotary frequency of ~40 Hz would be expected. Since a Chlamydomonas cell is seen to rotate with a frequency of only 1–2 Hz in our optical trap, and this motion is unconstrained, it appears that the total torque that is generated corresponds to the peak output of only about 5% of dynein molecules. The correspondence that we make here is only indicative, but it does seem to imply that the motor action of a randomly moving cell may be sustained by the combined action of only a subset of all available motor molecules. However, a cell that is highly constrained, or is undergoing directed motion by virtue of optical or chemical stimuli, may use the motoring action of much larger number of molecules. An alternate hypothesis is that there exists a ‘gear’ system that is capable of modulating the net output of dynein molecules during flagellar beating as a function of external load [15] (or internal signaling). The present results clearly indicate that much more experimental work is warranted in order that better insights are developed.

 

Fig. 4. Typical rotational frequencies for wild type and unflagellated Chlamydomonas cells.

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In summary, we have demonstrated the possibility of fabricating a readily controllable micromotor based on live, flagellated Chlamydomonas cells; flagellar translational motion is transduced into rotary action, giving rise to unusually large torque. Typical values that we measure for the force that is generated in our experiments have very important biological, biophysical, and biomedical implications.